#### Journal Title

Physical Review E

#### Publication Date

5-13-2009

#### Abstract

The dynamics of a spring-mass system under repeated impact with a vibrating wall is investigated using the static wall approximation. The evolution of the harmonic oscillator is described by two coupled difference equations. These equations are solved numerically, and in some cases exact analytical expressions have also been found. For a periodically vibrating wall, Fermi acceleration is only found at resonance. There, the average rebounding velocity increases linearly with the number of collisions. Near resonance, the average rebounding velocity grows initially with the number of collisions and eventually reaches a plateau. In the vicinity of resonance, the motion of the oscillator exhibits scaling properties over a range of frequency ratios. The presence of dissipation at resonance destroys the Fermi-acceleration process and induces scaling behavior similar to that at near resonance. For a moving wall with a random amplitude at collisions, Fermi acceleration is observed independently of the ratio between the wall and oscillator frequencies. In this case the average rebounding velocity grows with the square root of the number of collisions with the wall. Also, in this latter case, dissipation suppresses the Fermi-acceleration mechanism and induces a scaling behavior with the same universality class as that of the dissipative bouncing ball model with random external perturbations.

#### Subjects

Harmonic oscillators; Quantum theory

#### Citation: Pilot Scholars Version (Modified MLA Style)

Bonfim, O. F. de Alcantara, "Dynamical properties of an harmonic oscillator impacting a vibrating wall" (2009). *Physics Faculty Publications and Presentations*. 44.

https://pilotscholars.up.edu/phy_facpubs/44

#### DOI

10.1103/PhysRevE.79.056212

#### Peer-Reviewed

Yes

#### Document Type

Journal Article

## Publication Information

Physical Review E, 2009, Volume 79, Issue 5, 1-6.

© 2009 The American Physical Society

Archived version is the final published version.